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How to calculate fill time of free flooded offshore pipeline?


I have a problem I haven't been able to get answered yet, hopefully you can help out.

Basically, a pipeline is free flooded offshore at any given depth. Pipeline is laid empty at seabed, basically at atmospheric pressure inside. Free flooding meaning that one end is opened completely (gate valve or such). The other end is still closed or has a check valve to evacuate left over air.

I want to determine the fill time, or the velocity at which the pipeline is filled.

At first I was led to Bernoulli, but once the deep sea pressure diff was too high, the resulting velocities were too high (speed of sound). That has led me to choked flow, but I dont know how to apply it in this case.

It seems I need an application of Bernoulli, choked flow and head loss due to friction to complete, but dont know how to apply. Please help.



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